Tokyo stocks barely eked out a gain on Tuesday as enthusiasm about Sanae Takaichi, who is likely to be Japan's next prime minister, started to wane.

The Nikkei 225 stock average finished the day up 0.01% after hitting a record — of 48,527.33 — shortly after the open and then spending the rest of the day retracing its way back to where it started.

Takaichi was elected Saturday to succeed Prime Minister Shigeru Ishiba as the Liberal Democratic Party’s president. She is likely to become prime minister next week.

When the market opened on Monday after her election, stocks staged a powerful rally, ending the day up 4.75% on expectations that Takaichi will pursue economic stimulus and push the central bank to adopt an easy-money stance.

By Tuesday, traders and analysts started to take a closer look at the political realities she could face. They concluded that she could encounter some difficulties in implementing her agenda.

"I think there’s a growing sense of concern that Takaichi’s policies might struggle to move forward, and that’s starting to be seen as something of a risk,” said Takahide Kiuchi, executive economist at Nomura Research Institute.

The new prime minister will have to pull together a workable coalition, and that might require some compromises to appease other parties and potential partners.

News reports in the past two days indicated that Komeito might leave the existing coalition with the LDP, while the strong influence of former Prime Minister Taro Aso on appointments could lead to a watering down of some of Takaichi’s policies.

The reports also suggest that a working relationship with the Democratic Party for the People (DPP) is far from certain.

“Takaichi herself hasn’t really changed her policies, but the environment has," Kiuchi said. "She’s now leading a minority government, it’s unclear whether the coalition will hold together, cooperation with the DPP remains uncertain, Komeito might leave the coalition and Aso’s influence has grown stronger."

“The key question is how much these factors will constrain Takaichi’s original economic policies. That’s what everyone is watching most closely, and I think the financial markets will move more cautiously while keeping an eye on that.”

On Tuesday, the yen traded in a range around ¥150.5 to the dollar after a dramatic fall Monday, the first trading day after Takaichi's election.

Toyota, Japan's largest company by market capitalization, was up 1.65% on Tuesday, while Fast Retailing, which owns Uniqlo, fell 1.11%, and Tokyo Electron was down 1.31%.